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http://dx.doi.org/10.4134/BKMS.2015.52.2.593

UNIVARIATE LEFT FRACTIONAL POLYNOMIAL HIGH ORDER MONOTONE APPROXIMATION  

Anastassiou, George A. (Department of Mathematical Sciences University of Memphis)
Publication Information
Bulletin of the Korean Mathematical Society / v.52, no.2, 2015 , pp. 593-601 More about this Journal
Abstract
Let $f{\in}C^r$ ([-1,1]), $r{\geq}0$ and let $L^*$ be a linear left fractional differential operator such that $L^*$ $(f){\geq}0$ throughout [0, 1]. We can find a sequence of polynomials $Q_n$ of degree ${\leq}n$ such that $L^*$ $(Q_n){\geq}0$ over [0, 1], furthermore f is approximated left fractionally and simulta-neously by $Q_n$ on [-1, 1]. The degree of these restricted approximations is given via inequalities using a higher order modulus of smoothness for $f^{(r)}$.
Keywords
monotone approximation; Caputo fractional derivative; fractional linear differential operator; higher order modulus of smoothness;
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